Inducibility has natural extensions to directed graphs as well. Falgas-Ravry and Vaughan [1]} considered inducibility of small outstars, with an extension to all outstars by Huang in [2]} before being further generalized to other types of stars by Hu, Ma, Norin, and Wu [3]}. Orientations of short paths and the \(C_4\)  are explored in [4]} and [5]}, respectively. The inducibility of directed graphs on at most 4 vertices was explored in [6]}, and the corresponding tournaments were completely resolved in [7]}. Other recent work includes closing bipartite graphs on 5 vertices in [8]} and an exploration of inducibility for \(d\) -ary trees in [9]}.
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